Mesoscopic superfluid to superconductor transition

Abstract

Spectrum tomography for the energy ($E$) of a ring-shaped Bose-Hubbard circuit is illustrated. There is an inter-particle interaction $U$ that controls superfluidity (SF) and the transition to the Mott Insulator (MI) regime. The circuit is coupled to an electromagnetic cavity mode of frequency ${\omega }_0$, and the coupling is characterized by a generalized fine-structure-constant $\alpha$ that controls the emergence of superconductivity (SC). The $(U,\alpha ,{\omega }_0,E)$ diagram features SF and SC regions, a vast region of fragmented possibly chaotic states, and an MI regime for large $U$. The mesoscopic version of the Meissner effect and the Anderson-Higgs mechanism are discussed.

16 pages, 9 figures

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